Slice the chicken breasts in half horizontally to create four thin cutlets.

Place the cutlets between two sheets of plastic wrap and pound them to an even 1/4-inch thickness.

In a shallow dish, mix the flour, salt, and pepper.

Dredge each chicken cutlet in the flour mixture, shaking off any excess.

In a large skillet over medium-high heat, melt 2 tablespoons of butter with the olive oil.

When the butter is foaming, add the chicken cutlets (work in batches if necessary).

Cook for 3-4 minutes per side until golden brown and cooked through. Remove to a plate and tent with foil.

In the same skillet, add the lemon juice, chicken stock, and capers.

Bring to a boil, scraping up any browned bits from the bottom of the pan.

Simmer for 3-5 minutes until the liquid has reduced by half.

Whisk in the remaining 2 tablespoons of chilled butter until the sauce is thickened and glossy.

Stir in the fresh parsley.

Return the chicken to the pan and spoon the sauce over the top.

Garnish with lemon slices and serve immediately over pasta or with crusty bread.